Charhe question involving charge of rod and Length, help please?

[jcfor3ver]

Homework Statement

DESCRIPTION OF PROBLEM: So here is the problem (may look a little weird because I cannot input integral signs into this question)

A student working on a physics problem determined that the x- and y- components of the electric
field at a point P near a charged insulating rod can be calculated from the following integrals:

Homework Equations

KNOWN:
Note: K=constant and lambda=Q/L
dy=dervative of y

E,x=K*lambda (integral sign from 0 to length L) (dy/x^2+y^2)*(x/sq.rt(x^2+y^2))

which simplifies to E,x= K*lambda (integral from 0 to L) (x*dy/(x^2+y^2)^3/2)

Then E,y = -K*lambda (integral from 0 to L) (x*dy/(x^2+y^2)^3/2)

The Attempt at a Solution

SOLVE:
Now notice the negative in the y direction. What I drew my picture as was the rod parallel to y-axis and starting from y=0 some distance from a pt. P lying on the x-axis.

It asks me to find the Length, how should I do this? I did one thing where I set costheta=x/sq.rt(x^2+L^2) and solved for L, but I do not know if this is correct. Solving I received sq.rt((-x^2+(costheta/x))^2)=L

It also asks me to show how far point P is?
I am just confused on how to go about this, since it has both x and y components.
But I think it would be the same concept as finding L except solving for just x instead? I am confused. Help greatly appreciated!

 

[anathema]

Dear student,

Thank you for your question. It seems like you are on the right track with your solution. To find the length, you can use the Pythagorean theorem to relate the x and y components of the electric field at point P. This will give you an equation that relates the length L and the angle theta. From there, you can solve for L using the equation you derived for cos(theta).

As for finding the distance of point P from the rod, you can use the distance formula to find the distance between point P and the origin (where the rod starts). This will give you an equation with both x and y components, which you can then use to solve for the distance.

I hope this helps. Let me know if you have any further questions or if you need any clarification.